How many zeroes are there at the end of the following product?1 × 5 × 10 × 15 × 20 × 30 × 35 × 40 × 45 × 50 × 55 × 60

The number of zeroes at the end of a product is determined by the number of times 10 is a factor in the product. 10 is a product of 2 and 5.

In the given product, every number is a multiple of either 5 or 2 or both.

However, there are more multiples of 2 than 5. So, the limiting factor here is the number of 5s.

Let's count the multiples of 5 in the given product:

1 × 5(1) × 10(1) × 15(1) × 20(1) × 30(1) × 35(1) × 40(1) × 45(1) × 50(2) × 55(1) × 60(1)

The numbers in the brackets represent the count of factor 5 in the corresponding number. For example, 50 has two 5s as it is 552.

So, the total count of 5s is 1+1+1+1+1+1+1+1+1+2+1+1 = 12

Therefore, there are 12 zeroes at the end of the given product.